{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Pressure Broadening"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>© Von P. Walden, Washington State University</i>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Calculation of the Lorentz line shape, which approximates pressure broadening of atmospheric absorption/emission spectral lines."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Populating the interactive namespace from numpy and matplotlib\n"
     ]
    }
   ],
   "source": [
    "%pylab inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set the desired pressure and temperature.\n",
    "p  = 300.\n",
    "T  = 250."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "p0 = 1013.5                      # mb\n",
    "T0 = 273.15                      # K\n",
    "a0 = 0.5                         # Typical value for a0\n",
    "n  = 0.6                         # Typical value for n (I think)\n",
    "aL = a0 * (p/p0) * (T0/T)**n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.15607891010640065"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "aL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Lorentz Line Shape (pressure broadening)')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "varr = arange(-2,2,0.001)\n",
    "fL = (aL/pi)/(varr**2 + aL**2)\n",
    "\n",
    "plot(varr/aL,fL)\n",
    "xlabel('(v-v0)/aD')\n",
    "ylabel('Normalized f(v-v0)')\n",
    "title('Lorentz Line Shape (pressure broadening)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x10c627950>"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#legend(('1013 mb, 288 K','103.5 mb, 217 K','10.2 mb, 271 K','1.3 mb, 236 K'),loc='best')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<i>© Von P. Walden, Washington State University</i>"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "widgets": {
   "state": {},
   "version": "1.1.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
